Volume 2 Academic Career Chapter 767: From BSD Conjecture to Riemann Hypothesis
With a smile on his face, Chen Zhou hurried to the desk and sat down, gathering the draft papers on the desk together.
Although inspiration is unpredictable and no one knows when it will come, Chen Zhou always manages to have a sudden flash of inspiration at the critical moment and then seize this flash of inspiration.
In Chen Zhou’s own words, as long as you put in enough effort and have a solid foundation of basic knowledge.
Then in future research, even if you encounter difficult problems, you will not be completely clueless.
And among these possible clues to solve the problem, there will be that moment of inspiration.
As long as we catch it, the problem will be solved.
This is also Chen Zhou’s explanation for why he can always capture inspiration.
However, Chen Zhou never said that he had a collection of wrong questions that could help point to the only clue...
After carefully reading the draft papers, Chen Zhou's smile became more and more intense. This time he really grasped the inspiration to solve the BSD conjecture.
This was the first time that he had an idea to completely solve a problem just as he was about to go into seclusion.
Putting the stack of draft paper aside, Chen Zhou reached out and took a new stack of draft paper, then unscrewed the pen cap and began the final journey to solve the BSD conjecture.
Time passed day by day.
Chen Zhou and Xiong Hao have also returned to the state they were in at the beginning of this year.
One is an extreme research state, the other is an extreme state of bringing meals and taking care of people.
When seeing Xiong Hao like this, Cross and Chen Xiao surprisingly did not ask any more questions.
After all, with so much experience, I know what Chen Zhou is doing without asking.
Although the outside world believes that Chen Zhou has not achieved any research results in physics for such a long time, and even completely ignores the research time required for each research result.
Some people think that Chen Zhou has given up on the field of physics and that he is just a flash-in-the-pan physicist.
But Cross knew that these people were talking nonsense!
If more than a year is considered a long time, then how many physicists are there in this world?
Besides, after Chen Zhou opened the new door to physics, no one in the world could go deeper into the door of new physics than Chen Zhou's research.
This does not require new research results to prove this, but Chen Zhou’s previous paper on the new gauge field theory is enough to kill a group of physicists in seconds.
What's more, the research groups he and Gao Jie work in at the Institute of High Energy Physics both belong to Chen Zhou's research group.
Even if Chen Zhou rarely goes to the Institute of High Energy Physics, he can't ignore this fact, right?
How can it be said that Chen Zhou gave up his research in physics?
Even apart from these, Cross also knew that Chen Zhou was studying the grand unified theory of physics!
He heard it by chance, and therefore, Cross felt that Chen Zhou's retreat this time for research might be to solve the grand unified theory. Then let's see how these nonsense people will make it up!
Chen Zhou, who was buried in his desk and devoted himself to the research of BSD conjecture, naturally had no idea what Cross was thinking.
If you knew, you would probably laugh.
He was indeed planning to solve the grand unified theory, but this topic had not yet come to his attention.
…
"In the 1990s, Wiles and his student Taylor proved the semi-stable case of the Taniyama-Shimura-Weil conjecture, that is, the one-to-one correspondence between elliptic curves and 'modular forms', an important object in number theory."
"It allowed people to confirm the analytical extension of the L function on the entire complex plane and to write the L function in the form of a functional equation that is symmetric about s=1."
"And this work, which incidentally proved Fermat's Last Theorem, deepened people's understanding of L-functions and finally made the statement of the BSD conjecture, that is, the power series expansion of L-functions at s=1, meaningful..."
Chen Zhou couldn't help but feel a lot of emotion when thinking about what happened after the BSD conjecture was introduced into the L function and expressed using the L function.
Since the Langlands program, which had a profound influence on later generations, had not yet been proposed at that time, the profoundness of L functions in objects such as finite-dimensional Gavaro representations and automorphic representations had not been sufficiently revealed. Therefore, L functions were not used to express the original version of the BSD conjecture.
Even later, when the BSD conjecture introduced the L function and used the L function to express it, it was still a bold guess.
Because mathematicians at that time did not know much about L-functions, including the later knowledge of complex functions, which showed that the analytical extension is unique if it exists, which means that the L-function can be analytically extended to the entire complex plane, but this knowledge was not proven.
All I can say is that the BSD conjecture is also a mathematical conjecture with an ill-fated history.
And now, Chen Zhou is finally going to put this speculation to an end.
[…From this, it can be proved that ords=1(L(s,E))=rankz(E(K)) holds! ]
Finally, the BSD conjecture was solved. After completing and proving this conjecture, Chen Zhou did not feel relieved.
Instead, he frowned and looked at the entire proof process he had left on the draft paper.
I habitually tapped the draft paper with a pen, thinking about the things that made me feel wrong.
Suddenly, Chen Zhou stopped writing on the draft paper, put it aside, reached out and took the previous stack of draft papers, and began to search through them.
"I remember the original version, which was about the true value that the limit approaches..."
Chen Zhou was searching while muttering to himself.
He seemed to have found what was wrong, but he hadn't quite grasped it yet.
Finally, Chen Zhou found the draft paper and also found the place that made him feel something was wrong.
"Using an estimation method similar to the prime number theorem, we can prove that the true value approached by the limit in the original version of the BSD conjecture, whether or not it is equal to the algebraic rank, must be the number of repeated roots of the L function corresponding to the elliptic curve at s=1!"
"That is, after the L function is expanded into a power series at s=1, the power of the first non-zero term with a coefficient of (s-1) is the analytic rank..."
Chen Zhou looked at the draft paper in his hand and muttered to himself.
At the same time, many thoughts kept flashing through his mind.
In fact, what Chen Zhou muttered was referring to the BSD conjecture.
Because the official version of the BSD conjecture is that the analytic rank is equal to the algebraic rank.
However, what made Chen Zhou feel something was wrong was the original version of the BSD conjecture.
Because the conclusion of the original version is more profound, it not only contains the conclusion of the formal version, but also contains the Riemann hypothesis of the L function, that is, the real part of the zero point after the analytical extension of the L function is equal to the center of symmetry!
After a long time, Chen Zhou slowly put down the draft paper in his hand and looked at the stack of draft papers in another corner of the desk with some guilt.
That is about the research on the grand unified theory of physics.
"Well, wait a little longer. It won't take too long. Since the BSD conjecture gave me the inspiration for the Riemann hypothesis, I naturally don't want to let it go, right?"
After saying this silently, Chen Zhou picked up the pen again...
